1. Field of the Invention
The present invention relates to an exposure method for transferring a mask pattern on a plurality of shot areas arranged on a substrate through a projection optical system.
2. Related Background Art
In a projection exposure apparatus of a step and repeat type known as a stepper, a plurality of shot areas or chip pattern areas arranged on a substrate such as a semiconductor wafer or a glass plate are aligned in turn with predetermined positions, i.e., projection positions of a pattern of a mask (reticle) in stationary coordinates which are orthogonal coordinates defined by a pair of interferometers and which defines moving positions of the substrate. It is demanded that the alignment accuracy must always be high and stable in order to prevent the yield due to production of poor chips in the manufacturing process from being lowered. As disclosed in the U.S. Pat. Nos. 4,780,617 and 4,833,621, the enhanced global alignment method (EGA method) is mainly used to calculate the regularity of the shot arrangement on a wafer accurately by employing a statistical calculation in the stepper.
In the EGA method, the coordinate positions of only a plurality of shot areas-(three or more areas are required, normally about 10 to 15 areas) selected as sample shots on a single wafer are measured. After the coordinate positions of all the shot areas on the wafer are calculated from these measurement values using statistic calculation processing (method of least squares), stepping of a wafer stage is uniquely executed according to the calculated shot alignment. The EGA method requires only a shot measurement time, and an averaging effect for random measurement errors can be expected.
The statistic processing method used in the EGA method will be briefly described below. Designed alignment coordinates of m (m is an integer satisfying m.gtoreq.3) sample shots on a wafer are represented by (X.sub.n, Y.sub.n) (n=1, 2, . . . , m), and a linear model given by the following equation is assumed for a shift (.DELTA.X.sub.n, .DELTA.Y.sub.n) from the designed alignment coordinates. ##EQU1##
Furthermore, if actual alignment coordinates (measurement values) of the m sample shots are represented by (.DELTA.x.sub.n, .DELTA.y.sub.n), a square sum E of residuals obtained upon application of this model is expressed by: EQU E=.SIGMA.{(.DELTA.x.sub.n -.DELTA.X.sub.n).sup.2 +(.DELTA.y.sub.n -.DELTA.Y.sub.n).sup.2 } (2)
Thus, parameters a to f for minimizing this equation need only be obtained. In the EGA method, the alignment coordinates of all shot areas on a wafer are calculated on the basis of the parameters a to f calculated as described above and the designed alignment coordinates.
Since wafers are deformed during treatments such as heat treatment in the semiconductor production line, the size and thus the shape of shot areas on a wafer are also varied. If, therefore, the imaging optical characteristics of the projection optical system such as the projection magnification and the distortion are previously adjusted to the predetermined values and the shot areas are set at the exposure position by using the EGA method, the projection image of the reticle pattern and the shot areas are likely not to overlap accurately with each other over all ranges. In order to overcome this problem, there has been proposed a method in which a plurality of alignment marks on the reticle and a plurality of alignment marks on the wafer corresponding to them are detected by an alignment sensor employing the through-the-reticle method (TTR method), the magnification errors and then the distortion errors of the pattern image in the shot areas are obtained from the displacements between the corresponding marks, and the imaging optical characteristics of the projection optical system are adjusted so as to diminish these errors.
In the conventional technology, however, the magnification error and the distortion error of every shot area must be measured by means of the alignment sensor, and this lowers the throughput of the exposure apparatus. If any alignment marks attached to shot areas are broken in any treatment processes, the magnification errors and the distortion errors of the shot areas cannot be measured accurately, thereby lowering the overlapping accuracies between the shot areas and pattern images.
Furthermore, the EGA method processes shot alignment errors on a wafer as linear errors. In other words, the EGA calculation is a linear approximation. For this reason, the EGA method cannot cope with a variation in local alignment errors on a wafer, i.e., non-linear factors.